The vector product, also known as the cross product, is a fundamental operation in vector algebra that produces a vector perpendicular to both of the input vectors.
This concept is crucial in various fields of mathematics, physics, and engineering.
The vector product of two vectors $\mathbf{v}$ and $\mathbf{w}$ is defined as:
$$ \mathbf{v} \times \mathbf{w} = |\mathbf{v}|\,|\mathbf{w}|\,\sin\theta\,\hat{\mathbf{n}} $$
Where:
The direction of $\mathbf{n}$ is determined by the right-hand screw rule: if you curl the fingers of your right hand from $\mathbf{v}$ to $\mathbf{w}$ through the smaller angle, your thumb points in the direction of $\mathbf{n}$.
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